Question

An engine pump is used to pump a liquid of density ρ continuously through a pipe of cross-sectional area A. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy is being imparted to the liquid is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Energy supplied to liquid per second by the pump
$=\frac{1}{2}\frac{m{v}^2}{t}=\frac{1}{2}\frac{V\rho v^2}{t}=\frac{1}{2}A\times (\frac{1}{t})\times \rho \times v^2[\frac{l}{t}=v]$
$=\frac{1}{2}A\times v\times \rho \times v^2=\frac{1}{2}A\rho v^3$